Theorems · Definition · category theory

CategoryTheory.Preadditive.isWeakLimitKernelForkOfFork

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {X Y : C} →
        {f g : X ⟶ Y} →
          {c : CategoryTheory.Limits.Fork f g} →
            CategoryTheory.Limits.IsWeakLimit c →
              CategoryTheory.Limits.IsWeakLimit (CategoryTheory.Preadditive.kernelForkOfFork c)

A weak equalizer of f and g is a weak kernel of f - g.

Defined in: Mathlib.CategoryTheory.Limits.WeakLimits.WeakKernels
Cited by: 1 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.Limits.Forkstatement and proof · cited by 85
CategoryTheory.Limits.IsWeakLimitstatement and proof · cited by 23
CategoryTheory.Limits.IsWeakLimit.liftproof · cited by 8
CategoryTheory.Preadditive.forkOfKernelForkproof · cited by 8
CategoryTheory.Preadditive.kernelForkOfForkstatement and proof · cited by 7
CategoryTheory.Limits.Fork.IsWeakLimit.mk'proof · cited by 0

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Preadditive.hasWeakKernel_of_hasWeakEqualizerproof · cited by 0